One loop beta functions and fixed points in Higher Derivative Sigma Models

TL;DR

This paper computes one loop beta functions for higher derivative nonlinear sigma models in four dimensions, identifying fixed points and asymptotic safety conditions across different symmetry groups and derivative terms.

Contribution

It provides the first detailed analysis of fixed points in higher derivative sigma models, highlighting conditions for asymptotic safety in these theories.

Findings

Fixed points exist for all N ≥ 4 in O(N) models.

Fixed points are found only for N=2,3 in chiral SU(N) models.

Four derivative couplings are asymptotically free, two derivative coupling approaches a nonzero limit.

Abstract

We calculate the one loop beta functions for nonlinear sigma models in four dimensions containing general two and four derivative terms. In the O(N) model there are four such terms and nontrivial fixed points exist for all N \geq 4. In the chiral SU(N) models there are in general six couplings, but only five for N=3 and four for N=2; we find fixed points only for N=2,3. In the approximation considered, the four derivative couplings are asymptotically free but the coupling in the two derivative term has a nonzero limit. These results support the hypothesis that certain sigma models may be asymptotically safe.